Full-Space Approach to Aerodynamic Shape Optimization

DOI10.1016/J.COMPFLUID.2021.104843arXiv2011.13461MaRDI QIDQ6354665

Publication date: 26 November 2020

Abstract: Aerodynamic shape optimization (ASO) involves finding an optimal surface while constraining a set of nonlinear partial differential equations (PDE). The conventional approaches use quasi-Newton methods operating in the reduced-space, where the PDE constraints are eliminated at each design step by decoupling the flow solver from the optimizer. Conversely, the full-space Lagrange-Newton-Krylov-Schur (LNKS) approach couples the design and flow iteration by simultaneously minimizing the objective function and improving feasibility of the PDE constraints, which requires less iterations of the forward problem. Additionally, the use of second-order information leads to a number of design iterations independent of the number of control variables. We discuss the necessary ingredients to build an efficient LNKS ASO framework as well as the intricacies of their implementation. The LNKS approach is then compared to reduced-space approaches on a benchmark two-dimensional test case using a high-order discontinuous Galerkin method to discretize the PDE constraint.

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Newton-type methods (49M15) General aerodynamics and subsonic flows (76G25) Optimization of shapes other than minimal surfaces (49Q10) PDE constrained optimization (numerical aspects) (49M41)

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